Water-ice equilibrium Querry

Consider that we have ice and water together ( no heat exchange with surrounding ) and
qi1 = heat required by ice to reach 0 C from ti ( < 0 )
qi2 = heat required by ice at 0 C to convert into water at 0 C
qw = heat that can be released by water after reaching 0 C from tw ( > 0 )

No, your equation says that there is enough heat in the water to after it has reached 0 degrees to melt any ice in the water. In fact, all heat the water loses while dropping to 0 degrees would also contribute to melting the ice.

If you had set qw as the "heat contained by the water at tw" degrees and qi1+ qi2= qw then you would be "right on the verge" where whether there was a tiny amount of ice or not would depend on local effects. But is qi1+ qi2< qw or with your definition of qw as "heat still in the water after reaching 0 C", all ice will be melted.